pT HE INTERNATIONAL BESTSELLER 7 ®) q | the Parrot’s €orem DENIS CUEDI S| TRANSLATED BY FRANK WYNNE (£yj5..'', “A genuine insight into : the wonder of numbers.” ‘ i—SIMON SINGH, author of Fermat’s Engima eOeTReaOeEEE tTg TeSn e e Digitized by the Internet Archive in 2021 with funding from Kahle/Austin Foundation https://archive.org/details/parrotstheoremnoOO000gued The Parrot’s Theorem A Novel DENIS GUEDJ Translated by Frank Wynne THOMAS DUNNE BOOKS St. Martin’s Griffin #A New York THOMAS DUNNE BOOKS. An imprint of St. Martin’s Press. THE PARROT’S THEOREM. Copyright © 2000 by Denis Guedj. Translation © 2000 by Frank Wynne. All rights reserved. Printed in the United States of America. No part of this book may be used or reproduced in any manner whatsoever with- out written permission except in the case of brief quotations embodied in criti- cal articles or reviews. For information, address St. Martin’s Press, 175 Fifth Avenue, New York, N.Y. 10010. www.stmartins.com Library of Congress Cataloging-in-Publication Data Guedj, Denis. (Théoréme du perroquet. English] The parrot’s theorem: A novel / Denis Guedj ; translated by Frank Wynne. p. cm. ISBN 0-312-28055-6 (he) ISBN 0-312-30302-5 (pbk) I, Wynne, Frank. II. Title. PQ2667.U3555 T4813 2001 843'.914—de21 2001034891 First published in Great Britain by Weidenfeld & Nicolson First published in France by Editions du Seuil, Paris under the title Le Théoreme du Perroquet D109857: 6 95 Contents A Bird in the Hand 1 A curious parrot; a Euclidean family & two friends called Being and Nothingness Seen and Not Seen 10 A floating library & a family mystery The Glass Pyramid 16 Thales and the beginnings of mathematics; Mr Ruche lives dangerously & a visit to the pyramids The Rainforest Library 44 Books do furnish a room; an outline of the history of mathematics & a parrot without a passport The Three Ages of Maths 55 A cast of thousands & a well-eamed breakfast Friends and Enemies 65 A second letter; a suspicious death & Fermat’s Last Theorem The Numbers Game 76 The school of Pythagoras; a cult of secrecy & the music of numbers Just a Fraction 89 Irrational numbers; imaginary journeys & proving the impossible Night Boat to Alexandria 98 Black tie; white sands & an introduction to Euclid’s Elements 10 One Risotto and a Chicken Korma 118 Apollonius and Hipparchus; trigonometry unleashed; a good argument & a significant curry 11 Problems, Problems, Problems 132 A plague in Athens; Hippias, Hippocrates and Plato & the three great mathematical problems of the ancient world 12 The Great Glass Elevator 142 Mathematics in the Arab world; poetry and algebra & Omar Khayyam 13 The story of © 1S1 The power of zero; Brahmagupta and al-Khwarizmi & a tea ceremony 14 The Fifth Postulate 165 A gangster in Tokyo; Menelaus and Nasir al-Din al-Tusi; trigonometry explained & a fortunate barrow us Secrets and Lies 182 Fibonacci’s numbers; Tartaglia, Cardano and Ferrari; back to zero & the hunt for Max Liard 16 Less is More 195 Signs and symbols; imaginary numbers & solving Cardano’s equation 17 Fame! 207 Niels Abel and Evariste Galois; the Paris Institute & the long-awaited proof 18 Between the Infinite and the Void 220 Descartes, Pascal and Fermat; analytical geometry and number theory; Newton and Leibniz & differential and integral calculus a A Narrow Margin 240 Pascal and probability; number theory & Fermat’s Last Theorem 20 A Handful of Feathers 252 nt in the sky; Euler and the magical number e; John Napier and logarithms & a fit of apoplexy [vi] 2! The Proof of the Pudding 274 Goldbach’s conjecture; Fermat’s second theorem; unrequited love & how Fermat’s Last Theorem saved a man’s life 22 In Mathematics, Nothing is Impossible 280 The three great problems of Greek mathematics & a nasty surprise Pe) The Third Man 289 The third member of the trio; a secret gallery & Grosrouvre’s loyal friend 24 Less is More 304 Archimedes; the siege ofS yracuse; the beginnings of ballistics & a failed attempt 25 Clear Blue Sky S27 High above the rainforest; a solitary bird & a death in the afternoon 26 Stepping Stones 334 A family reunion; a toast to Sidney & some explanations Epilogue 338 The conference of the birds Cast of characters 339 [vii] For Bertrand Marchadier Thanks to Brigitte, Jacques Binsztok, Jean Brette, Christian Houzel, Jean-Marc Lévy-Leblond, Isabelle Stengers.